1 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all occupants of all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings (or occupants) was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.

2 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate:

3 RSEs for estimates from the MPS are published for the first time in 'direct' form. Previously a statistical model was produced that relates the size of estimates to their corresponding RSEs, and this information was displayed via an 'SE table'. From this point onwards, RSEs for MPS estimates have been calculated for each separate estimate and published individually. The Jackknife method of variance estimation is used for this process, which involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the original sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the published estimate.

4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication, only those for Table 1 have been included at the end of these Technical Notes (see section 'Relative Standard Errors'). However, RSEs for all these estimates are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Work in Selected Culture and Leisure Activities, Australia, April 2007(cat. no. 6281.0).

5 Table 13 includes information for previous surveys: 1993, 1997, 2001 and 2004. The RSEs for these surveys were calculated using the previous modelled approach and are available from the relevant issue of Work in Selected Culture and Leisure Activities, Australia(cat. no. 6281.0) on the ABS web site <www.abs.gov.au>.

6 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate that they are considered too unreliable for general use.

CALCULATION OF STANDARD ERROR

7 SEs can be calculated using the estimates (counts or means) and the corresponding RSEs. For example Table 1 shows that the estimated number of persons in South Australia involved in selected culture and leisure activites in the previous 12 months was 294,300. In the corresponding RSE table (see 'Relative Standard Errors' at the end of these Technical Notes), the RSE for this estimate is shown to be 3.4%. The SE is:

= 0.034 * 294,300
= 10,000 (rounded to nearest 100)

8 Therefore there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall within the range 284,300 to 304,300 and about 19 chances in 20 that the value will fall within the range 274,300 to 314,300. This example is illustrated below.

PROPORTIONS AND PERCENTAGES

9 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.

10 For example in Table 1, the estimate for the total number of persons in Queensland who had some involvement in selected culture or leisure activities in the previous 12 months was 680,100. The estimated number of persons in Queensland who had some paid involvement in selected culture and leisure activities in the the previous 12 months was 205,300, so of those persons involved in selected culture and leisure activities in Queensland, the proportion paid for their involvement is (205,300 / 680,100)*100 or 30.2%.

11 From the RSE table for Table 1 (see 'Relative Standard Errors' at the end of these Technical Notes) the RSE of the total number of persons in Queensland who worked in selected culture and leisure activities is 2.9% and the RSE of the estimated number of these persons that had some paid involvement is 6.1%.
Applying the above formula, the RSE of the proportion is

12 This then gives an SE of the percentage (30.2%) of (5.4/100)*30.2 = 1.6 percentage points.

13 Therefore there are about two chances in three that the proportion of persons in Queensland who worked in selected culture and leisure activities and had some paid involvement is between 28.6% and 31.8% and 19 chances in 20 that the proportion is within the ranges 27.0% and 33.4%.

DIFFERENCES

14 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:

SIGNIFICANCE TESTING

15 The statistical significance test for any of the comparisons between estimates was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 14. This standard error is then used to calculate the following test statistic:

16 If the value of this test statistic is greater than 1.96 then we may say there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.

17 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design or questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.